The authors present a cascadable circuit for the distance metric and nonlinear functions required by radial basis function (RBF) neural networks. The distance metric is a quadratic approximation to the Euclidean distance between two voltages, and the nonlinearity is produced using two MOS transistors. This circuit has been developed for pulse stream neural systems. The operation of the circuit is described and suggestions are made for its practical implementation in pulsed analogue VLSI. Since the nonlinearity generated by the circuit has not been used in RBFs before, software results are presented to demonstrate that the circuit can produce good classification performance. However, software simulations show that the shape of the nonlinearity has implications for the performance of RBFs using the circuit. The authors consider the implications of these results to the development of pulsed analogue RBF chips in the limited precision environment of analogue VLSI. Based on their findings, they make suggestions for the shape and range of future centre circuits to make them robust to this limited precision and which they believe will help ensure good classification performance is obtained in hardware